Development of a Fuzzy Probabilistic Methodology for Multiple-Site Fatigue Damage

Abstract

A strategy for fuzzy-probabilistic assessment of the impact of multiple-site fatigue damage (MSD) on the fatigue resistance of aging structures is developed. The residual strength of a structure may be significantly reduced by the existence of fatigue damage at multiple locations. Depending on the level of knowledge with which they are known, MSD-related parameters may be represented as either purely random variables or fuzzy random variables. The membership functions of the probabilistic characteristics of fuzzy random variables, namely, mean values and standard deviations are developed. Mechanistic and probabilistic models used to evaluate multi-site fatigue damage are also presented. A probabilistic solution strategy, employing a first-order reliability method, is combined with a response-surface-based fuzzy modeling approach to construct the possibility distributions of the probabilistic safety indicators (namely, reliability indices and failure probabilities) for components subjected to multiple-site fatigue damage. Instead of providing the traditional single-valued, purely probabilistic measure for reliability, the present formulation proves its merit in its ability to combine experimental data with expert knowledge to provide confidence bounds on the structural integrity of aging structures. Moreover, the predicted bounds are dependent on the level of knowledge regarding the fuzzy input parameters, with a greater knowledge producing more narrow bounds. An example problem is used to demonstrate the advantages of the proposed methodology.